CAT 2022 Slot 1 — DILR Question 3
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Given above is the schematic map of the metro lines in a city with rectangles denoting terminal stations (e.g. A), diamonds denoting junction stations (e.g. R) and small filled-up circles denoting other stations. Each train runs either in east-west or north-south direction, but not both. All trains stop for 2 minutes at each of the junction stations on the way and for 1 minute at each of the other stations. It takes 2 minutes to reach the next station for trains going in east-west direction and 3 minutes to reach the next station for trains going in north-south direction. From each terminal station, the first train starts at 6 am; the last trains leave the terminal stations at midnight. Otherwise, during the service hours, there are metro service every 15 minutes in the north-south lines and every 10 minutes in the east west lines. A train must rest for at least 15 minutes after completing a trip at the terminal station, before it can undertake the next trip in the reverse direction. (All questions are related to this metro service only. Assume that if someone reaches a station exactly at the time a train is supposed to leave, (s)he can catch that train.)
Haripriya is expected to reach station S late. What is the latest time by which she must be ready to board at station S if she must reach station B before 1 am via station R?
Answer & solution
- A
11:35 pm
- B
11:49 am
11:39 pm
- D
11:43 pm
Route taken by Haripriya: S → R → B
Time taken from S → R:
Travel time = 10 × 2 = 20 mins
Stoppage time = 9 × 1 = 9 mins
Total time = 20 + 9 = 29 mins
Similarly, Time taken from R → B: 7 × 3 + 7 = 28 mins
In the north-south direction, the first train from A arrives at R at time = 6 am + (3 × 3) + (2 × 1) mins = 6:11 am.
Since R is a junction so this train will halt for 2 minutes at R and leave at 6:13.
Every 15 minutes, a train starts from A in the north-south direction.
The last train that leaves A will be at 12:00 am and it will leave R at 12:13 am, so Haripriya must reach R till 12:13 am.
If she catches this train from R at 12:13, she will reach B by 12:13 + 28 = 12:41 am.
Travelling time between S and R = (10 × 2) + (9 × 1) = 29
So Haripriya must board the train at S by (12:13 - 29 =) 11:44 pm
In the east-west direction, the first train from N arrives at S at time = 6 am + (6 × 2) + (5 × 1) = 6:17 am.
Since S is a junction so this train will halt for 2 minutes at S and leave at 6:19.
Every 10 minutes, a train starts from N in the east-west direction.
Therefore, Haripriya should board the train which leaves S at 11:39.
âââââââHence, option (c).